Modern Multivariate Statistical Techniques Regression, Classification, and Manifold Learning

Name: Modern Multivariate Statistical Techniques Regression, Classification, and Manifold Learning
Availability: InStock
ISBN: 9780387781884

ISBN-10: 0387781889

ISBN-13: 9780387781884

Edition: 2008

Authors: Alan Julian Izenman

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Book details

List price: $129.99
Copyright year: 2008
Publisher: Springer New York
Publication date: 8/28/2008
Binding: Hardcover
Pages: 733
Size: 6.10" wide x 9.25" long x 1.50" tall
Weight: 3.498
Language: English



Preface



Introduction and Preview



Multivariate Analysis



Data Mining



From EDA to Data Mining



What Is Data Mining?



Knowledge Discovery



Machine Learning



How Does a Machine Learn?



Prediction Accuracy



Generalization



Generalization Error



Overfitting



Overview of Chapters


Bibliographical Notes



Data and Databases



Introduction



Examples



Example: DNA Microarray Data



Example: Mixtures of Polyaromatic Hydrocarbons



Example: Face Recognition



Databases



Data Types



Trends in Data Storage



Databases on the Internet



Database Management



Elements of Database Systems



Structured Query Language (SQL)



OLTP Databases



Integrating Distributed Databases



Data Warehousing



Decision Support Systems and OLAP



Statistical Packages and DBMSs



Data Quality Problems



Data Inconsistencies



Outliers



Missing Data



More Variables than Observations



The Curse of Dimensionality


Bibliographical Notes


Exercises



Random Vectors and Matrices



Introduction



Vectors and Matrices



Notation



Basic Matrix Operations



Vectoring and Kronecker Products



Eigenanalysis for Square Matrices



Functions of Matrices



Singular-Value Decomposition



Generalized Inverses



Matrix Norms



Condition Numbers for Matrices



Eigenvalue Inequalities



Matrix Calculus



Random Vectors



Multivariate Moments



Multivariate Gaussian Distribution



Conditional Gaussian Distributions



Random Matrices



Wishart Distribution



Maximum Likelihood Estimation for the Gaussian



Joint Distribution of Sample Mean and Sample Covariance Matrix



Admissibility



James-Stein Estimator of the Mean Vector


Bibliographical Notes


Exercises



Nonparametric Density Estimation



Introduction



Example: Coronary Heart Disease



Statistical Properties of Density Estimators



Unbiasedness



Consistency



Bona Fide Density Estimators



The Histogram



The Histogram as an ML Estimator



Asymptotics



Estimating Bin Width



Multivariate Histograms



Maximum Penalized Likelihood



Kernel Density Estimation



Choice of Kernel



Asymptotics



Example: 1872 Hidalgo Postage Stamps of Mexico



Estimating the Window Width



Projection Pursuit Density Estimation



The PPDE Paradigm



Projection Indexes



Assessing Multimodality


Bibliographical Notes


Exercises



Model Assessment and Selection in Multiple Regression



Introduction



The Regression Function and Least Squares



Random A Case



Fixed A Case



Example: Bodyfat Data



Prediction Accuracy and Model Assessment



Random-X Case



Fixed- X Case



Estimating Prediction Error



Apparent Error Rate



Cross-Validation



Bootstrap



Instability of LS Estimates



Biased Regression Methods



Example: PET Yarns and NIR Spectra



Principal Components Regression



Partial Least Squares Regression



Ridge Regression



Variable Selection



Stepwise Methods



All Possible Subsets



Criticisms of Variable Selection Methods



Regularized Regression



Least Angle Regression



The Forwards Stagewise Algorithm



The LARS Algorithm


Bibliographical Notes


Exercises



Multivariate Regression



Introduction



The Fixed-X Case



Classical Multivariate Regression Model



Example: Norwegian Paper Quality



Separate and Multivariate Ridge Regressions



Linear Constraints on the Regression Coefficients



The Random-X Case



Classical Multivariate Regression Model



Multivariate Reduced-Rank Regression



Example: Chemical Composition of Tobacco



Assessing the Effective Dimensionality



Example: Mixtures of Polyaromatic Hydrocarbons



Software Packages


Bibliographical Notes


Exercises



Linear Dimensionality Reduction



Introduction



Principal Component Analysis



Example: The Nutritional Value of Food



Population Principal Components



Least-Squares Optimality of PCA



PCA as a Variance-Maximization Technique



Sample Principal Components



How Many Principal Components to Retain?



Graphical Displays



Example: Face Recognition Using Eigenfaces



Invariance and Scaling



Example: Pen-Based Handwritten Digit Recognition



Functional PCA



What Can Be Gained from Using PCA?



Canonical Variate and Correlation Analysis



Canonical Variates and Canonical Correlations



Example: COMBO-17 Galaxy Photometric Catalogue



Least-Squares Optimality of CVA



Relationship of CVA to RRR



CVA as a Correlation-Maximization Technique



Sample Estimates



Invariance



How Many Pairs of Canonical Variates to Retain?



Projection Pursuit



Projection Indexes



Optimizing the Projection Index



Visualizing Projections Using Dynamic Graphics



Software Packages


Bibliographical Notes


Exercises



Linear Discriminant Analysis



Introduction



Example: Wisconsin Diagnostic Breast Cancer Data



Classes and Features



Binary Classification



Bayes's Rule Classifier



Gaussian Linear Discriminant Analysis



LDA via Multiple Regression



Variable Selection



Logistic Discrimination



Gaussian LDA or Logistic Discrimination?



Quadratic Discriminant Analysis



Examples of Binary Misclassification Rates



Multiclass LDA



Bayes's Rule Classifier



Multiclass Logistic Discrimination



LDA via Reduced-Rank Regression



Example: Gilgaied Soil



Examples of Multiclass Misclassification Rates



Software Packages


Bibliographical Notes


Exercises



Recursive Partitioning and Tree-Based Methods



Introduction



Classification Trees



Example: Cleveland Heart-Disease Data



Tree-Growing Procedure



Splitting Strategies



Example: Pima Indians Diabetes Study



Estimating the Misclassification Rate



Pruning the Tree



Choosing the Best Pruned Subtree



Example: Vehicle Silhouettes



Regression Trees



The Terminal-Node Value



Splitting Strategy



Pruning the Tree



Selecting the Best Pruned Subtree



Example: 1992 Major League Baseball Salaries



Extensions and Adjustments



Multivariate Responses



Survival Trees



MARS



Missing Data



Software Packages


Bibliographical Notes


Exercises



Artificial Neural Networks



Introduction



The Brain as a Neural Network



The McCulloch-Pitts Neuron



Hebbian Learning Theory



Single-Layer Perceptrons



Feedforward Single-Layer Networks



Activation Functions



Rosenblatt's Single-Unit Perceptron



The Perceptron Learning Rule



Perceptron Convergence Theorem



Limitations of the Perceptron



Artificial Intelligence and Expert Systems



Multilayer Perceptrons



Network Architecture



A Single Hidden Layer



ANNs Can Approximate Continuous Functions



More than One Hidden Layer



Optimality Criteria



The Backpropagation of Errors Algorithm



Convergence and Stopping



Network Design Considerations



Learning Modes



Input Scaling



How Many Hidden Nodes and Layers?



Initializing the Weights



Overfitting and Network Pruning



Example: Detecting Hidden Messages in Digital Images



Examples of Fitting Neural Networks



Related Statistical Methods



Projection Pursuit Regression



Generalized Additive Models



Bayesian Learning for ANN Models



Laplace's Method



Markov Chain Monte Carlo Methods



Software Packages


Bibliographical Notes


Exercises



Support Vector Machines



Introduction



Linear Support Vector Machines



The Linearly Separable Case



The Linearly Nonseparable Case



Nonlinear Support Vector Machines



Nonlinear Transformations



The ""Kernel Trick""



Kernels and Their Properties



Examples of Kernels



Optimizing in Feature Space



Grid Search for Parameters



Example: E-mail or Spam?



Binary Classification Examples



SVM as a Regularization Method



Multiclass Support Vector Machines



Multiclass SVM as a Series of Binary Problems



A True Multiclass SVM



Support Vector Regression



e-Insensitive Loss Functions



Optimization for Linear ϵ-Insensitive Loss



Extensions



Optimization Algorithms for SVMs



Software Packages


Bibliographical Notes


Exercises



Cluster Analysis



Introduction



What Is a Cluster?



Example: Old Faithful Geyser Eruptions



Clustering Tasks



Hierarchical Clustering



Dendrogram



Dissimilarity



Agglomerative Nesting (agnes)



A Worked Example



Divisive Analysis (diana)



Example: Primate Scapular Shapes



Nonhierarchical or Partitioning Methods



i-Means Clustering (kmeans)



Partitioning Around Medoids (pam)



Fuzzy Analysis (fanny)



Silhouette Plot



Example: Landsat Satellite Image Data



Self-Organizing Maps (SOMs)



The SOM Algorithm



On-line Versions



Batch Version



Unified Distance Matrix



Component Planes



Clustering Variables



Gene Clustering



Principal Component Gene Shaving



Example: Colon Cancer Data



Block Clustering



Two Way Clustering of Microarray Data



Biclustering



Plaid Models



Example: Leukemia (ALL/AML) Data



Clustering Based Upon Mixture Models



The EM Algorithm for Finite Mixtures



How Many Components?



Software Packages


Bibliographical Notes


Exercises



Multidimensional Scaling and Distance Geometry



Introduction



Example: Airline Distances



Two Golden Oldies



Example: Perceptions of Color in Human Vision



Example: Confusion of Morse Code Signals



Proximity Matrices



Comparing Protein Sequences



Optimal Sequence Alignment



Example: Two Hemoglobin Chains



String Matching



Edit Distance



Example: Employee Careers at Lloyds Bank



Classical Scaling and Distance Geometry



From Dissimilarities to Principal Coordinates



Assessing Dimensionality



Example: Airline Distances (Continued)



Example: Mapping the Protein Universe



Distance Scaling



Metric Distance Scaling



Metric Least-Squares Scaling



Sammon Mapping



Example: Lloyds Bank Employees



Bayesian MDS



Nonmetric Distance Scaling



Disparities



The Stress Function



Fitting Nonmetric Distance-Scaling Models



How Good Is an MDS Solution?



How Many Dimensions?



Software Packages


Bibliographical Notes


Exercises



Committee Machines



Introduction



Bagging



Bagging Tree-Based Classifiers



Bagging Regression-Tree Predictors



Boosting



AdaBoost: Boosting by Reweighting



Example: Aqueous Solubility in Drug Discovery



Convergence Issues and Overfitting



Classification Margins



AdaBoost and Maximal Margins



A Statistical Interpretation of AdaBoost



Some Questions About AdaBoost



Gradient Boosting for Regression



Other Loss Functions



Regularization



Noisy Class Labels



Random Forests



Randomizing Tree Construction



Generalization Error



An Upper Bound on Generalization Error



Example: Diagnostic Classification of Four Childhood Tumors



Assessing Variable Importance



Proximities for Classical Scaling



Identifying Multivariate Outliers



Treating Unbalanced Classes



Software Packages


Bibliographical Notes


Exercises



Latent Variable Models for Blind Source Separation



Introduction



Blind Source Separation and the Cocktail-Party Problem



Independent Component Analysis



Applications of ICA



Example: Cutaneous Potential Recordings of a Pregnant Woman



Connection to Projection Pursuit



Centering and Sphering



The General ICA Problem



Linear Mixing: Noiseless ICA



Identifiability Aspects



Objective Functions



Nonpolynomial-Based Approximations



Mutual Information



The FastICA Algorithm



Example: Identifying Artifacts in MEG Recordings



Maximum-Likelihood ICA



Kernel ICA



Exploratory Factor Analysis



The Factor Analysis Model



Principal Components FA



Maximum-Likelihood FA



Example: Twenty-four Psychological Tests



Critiques of MLFA



Confirmatory Factor Analysis



Independent Factor Analysis



Software Packages


Bibliographical Notes


Exercises



Nonlinear Dimensionality Reduction and Manifold Learning



Introduction



Polynomial PCA



Principal Curves and Surfaces



Curves and Curvature



Principal Curves



Projection-Expectation Algorithm



Bias Reduction



Principal Surfaces



Multilayer Autoassociative Neural Networks



Main Features of the Network



Relationship to Principal Curves



Kernel PCA



PCA in Feature Space



Centering in Feature Space



Example: Food Nutrition (Continued)



Kernel PCA and Metric MDS



Nonlinear Manifold Learning



Manifolds



Data on Manifolds



Isomap



Local Linear Embedding



Laplacian Eigenmaps



Hessian Eigenmaps



Other Methods



Relationships to Kernel PCA



Software Packages


Bibliographical Notes


Exercises



Correspondence Analysis



Introduction



Example: Shoplifting in The Netherlands



Simple Correspondence Analysis



Two-Way Contingency Tables



Row and Column Dummy Variables



Example: Hair Color and Eye Color



Profiles, Masses, and Centroids



Chi-squared Distances



Total Inertia and Its Decomposition



Principal Coordinates for Row and Column Profiles



Graphical Displays



Square Asymmetric Contingency Tables



Example: Occupational Mobility in England



Multiple Correspondence Analysis



The Multivariate Indicator Matrix



The Burt Matrix



Equivalence and an Implication



Example: Satisfaction with Housing Conditions



A Weighted Least-Squares Approach



Software Packages


Bibliographical Notes


Exercises


References


Index of Examples


Author Index


Subject Index